Good reduction of Jacobians of twisted Fermat curves

Thomas · science forum beginner Joined: 28 Apr 2005 Posts: 3

Hello,

question about twisted Fermat curves.

Let p > 3 be a prime number, and let a,b,c be pairwise coprime integers not divisible by p.
Let l \neq p be a prime dividing abc.

Let F be the curve a x^p + bx^p + cx^p.
and let J be its Jacobian.

Are there inegers a,b,c such that for all l | abc the Jacobian J has good reduction at l ?

Thank you
T.

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